Wavelet analysis of vortex dynamics in 3D rotating helical turbulence


We introduce four novel methods to analyze joint location-scale energetics (i.e., energy, enstrophy, helicity and Lamb-vector distributions), for turbulent flows with intermediate-scale helical Beltrami forcing. Our data are direct numerical simulations on up to 15363 grid points with Reynolds numbers above 5600, with or without imposed rotation down to Rossby number 0.06. Using a classical method, we decompose the flow into orthogonal coherent and incoherent parts: the former always comprises less than 5% of the wavelets, almost all energy, and an enstrophy share depending on the vorticity distribution; the latter is noisy, much less space-filling in the helical rotating case, and very weak near the strong Beltrami coherent-vortices (BCV) formed in rotating helical flows. Two-dimensionalization is indicated by weak incoherent vertical-velocity kurtosis. Coherent parts account for almost all the energy and helicity spectra, while incoherent parts suggest equipartition in a statistical-equilibrium sense (Kraichnan 1973). The threshold defining (in)coherent partition varies strongly between experiments. Our novel methods are: 1, 4D location-scale energetics, showing extrema at all scales, at 3D locations enabling physical interpretation; 2, to identify Lamb-vector spectrum as rotational momentum transfer between phase-space atoms; 3, to sum partially that vector transfer over scale, to get a spatially localized vector flux across scales; and 4, to average azimuthally to get a radially dependent wavelet spectrum. Method 3 reveals the spatial structure of upscale vector-momentum transfers related to structures near the BCV, and method 4 quantifies increasing smoothness of BCV with decreasing distance to its core.

Mar 31, 2015 3:30 PM — 4:30 PM
Bechtel Collaboratory, Discovery Learning Center
Engineering Center, University of Colorado at Boulder, Boulder, CO 80309